A Statistical Abstract Analysis of the Gelman Paradox: Why correlation does not denote causation in voting outcomes based on regional average incomes John W, PhD Peru State College Dr. Andrew Gelman Ph.D. a statistician and political science expert from Columbia University is the person for whom the Gelman Paradox is named. Dr. Gelman as has reputation in Academic circles as a scholar. He is also known in the mainstream press by such publications as the New York Times, Time Magazine, NewsWeek, and The Washington Post. Gelman (2008) found voting patterns are most strongly influenced by income. Although many of those in the lower socio-economic group tend to be socially conservative, they do not tend to vote for the more socially conservative candidate; however, they do tend to vote based on economic issues (Huber & Stanig, 2009). Over the past few years the formerly solid south for Democrats has shifted toward being more reliably Republican. A look at correlations, without analyzing the data, gives the incorrect view that many regions with very low incomes and many poor social conservatives tend to vote Republican; however, an analysis of the data shows those low income voters are actually voting for the Democratic Party. What is responsible for this apparent paradox? Gelman (2012) discovered the richer and better educated (have a college degree) in the United States tend to vote Republican while those with lower incomes and less education (do not have a college degree) tend to vote for Democrats.
However, there are exceptions. For example, Gelman discovered eighty percent of those who are wealthy because they are trust fund kids do vote for the Democrats. It could also be argued some billionaires tend to support the Democratic Party because their businesses are reliant on contracts with the government and government spending. However, the general trend is the better educated and the wealthier tend to vote for the Republican Party. People employed by government, and therefore paid with taxpayer dollars, may also favor the Democratic Party. Please keep this caveat in mind, there is no single cause as to why anyone does or does not vote for a political party. Additionally, the Gelman Paradox is looking at general trends rather than at specific elections. The likability or affinity a voter may have for a particular candidate, tradition, friends, family, opinions about social favorability, sources of income, career field, and many other factors are a component as to why people vote the way they vote. A great number of people vote for both parties depending on a plethora of factors, depending on whether or not the election is local, statewide, or national, many voters may split their ticket, and there are other factors related to voting. But what about the Southern part of the United States? The poorer areas tend to support Republicans. Is this because the voters there are poor and uneducated as was suggested by a post I saw on social media? The answer is of course no. The poor, even in the south, and even poor areas where the majority of the vote goes to the Republicans, do tend to vote overwhelmingly for the Democratic Party. The middle class and the rich tend to vote for the Republicans. The advancement of the middle class in the South is the reason for the shift of the Southern States in the USA from the solid Democratic column to the Republican column. Inquiries & Perspectives 86
But wait, if a majority of the poor do not vote for the Republican then how can a poor district find itself voting for the Republican candidate? This is because of voting percentages of rich, middle class, and poor and as a result of the Southern United States seeing economic growth and developing a larger middle class starting in the 1980s. However, income inequality is a basis for class based voting (McCarty, Poole, and Rosenthal, 2006). What about religious values? Regardless of religious values the wealthier tend to vote Republican while the poor tend to vote for the Democrat; the difference is voter turn-out as Republicans enjoy a greater turnout of voters than the Democrats (Gelman, Kenworthy, & Su, 2010). In other words, there was no statistically significant difference in voting patterns related to religions values. Statistical Abstract Suppose there is a small voting precinct having 200 registered voters. These numbers roughly correspond with accepted polling data but are not exact. The point of the model is to demonstrate how the paradox operates not to show exact numbers. Therefore, this model is a statistical abstract to demonstrate why a paradox occurs. Of people at the poverty line ($15,000 per year) only about 45% vote. Suppose 100 or half of the people in this precinct are below the poverty line and they all vote for the Democratic candidate. This provides 45 votes for the democratic candidate. The next group are the low middle class ($30,000 a year). There are 55 people meeting this criterion in this precinct. This group votes equally for the democratic candidate and the Inquiries & Perspectives 87
Republican candidate. About 60 percent of the people in this group vote. This provides 17 Democratic votes and 16 Republican votes. Of course in actuality this would be 16.5 votes to the Democratic candidate and to the Republican candidate. Because we cannot have half of a voter we will say the Democratic candidate gets the extra voter. There are 45 people in the middle middle class making about $50,000 per year and they vote at a rate of about seventy-five percent and they vote Republican. This gives 33.75 votes to the Republican candidate. Because we can t have 75% of a voter we will call this 33 votes. The average income for this precinct is about $27,000 per voter, and is below lower middle class. If you figure in the per capita based on size of household, then the average income per capita is even lower and could be below our poverty line of 15,000. For example, say there is one child per one voter. Now we have a per capita income of 13,500 per year. This is a very poor precinct. Population and People s Low 100 15,000 1,500,000 Low Middle 55 30,000 1,650,000 Middle Middle 45 50,000 2,250,000 200 5,400,000 Per Capita Voters 200 27,000 Citizens 400 13,500 Per Capita Per Voter Per Capita Per Population Inquiries & Perspectives 88
The election results are now 56% from the Democratic candidate and 44% for the Republican candidate. Before the rise of the middle class in the South Voters Voters Percentage Voting Democratic Republican Low 100 45% 45 45 Low Middle 55 60% 17 16 33 Middle Middle 45 75% 33 33 s 200 56% 62 49 111 Percentage of the vote 56% 44% 100% Now we see the middle class start to grow. There are now still 90 voters at the poverty line, 50 voters in the lower middle class and 60 voters middle-middle class (this could also be interpreted as increasing income inequality). Population and New Levels People s Low 90 15,000 1,350,000 Low Middle 50 30,000 1,500,000 Middle Middle 60 50,000 3,000,000 200 5,850,000 New Per Capita Voters 200 29250 Citizens 400 14625 Per Capita Per Voter Per Capita Per Population After the rise of the middle class in the South Voters Voters Percentage Voting Democratic Republican Low 90 45% 41 41 Low Middle 50 60% 15 15 30 Middle Middle 60 75% 45 45 s 200 58% 56 60 116 Percentage of the vote 48% 52% 100% Inquiries & Perspectives 89
The increase in total income has gone from 5,400,000 dollars to 5,850,000 dollars representing an increase of 450,000 dollars. The new result would calculate as an increase of 1,125 dollar per capita or 2,250 dollar per voter in income. In other words, after a 1,125 dollar increase in per capita income per year we still have the per capita income of $14,625. So, the average income per capita is below our $15,000 poverty line and has not increased very much at all. But now let us look at the election results. Now we have 48% voting for the Democratic Party and 52% voting for the Republican Party (90 at 45%, 50 at 60% and 60 at 75%). Although this precinct is still below the poverty line it has gone from being a solid safe precinct for the Democratic Party to being a solid by 4% of the vote for the Republican Party. This would be reported as the precinct below the poverty line having a 14% change in voter preference toward the Republicans after only a 1,125 dollar per year per capita increase in income. This amounts to 93.75 dollars a month increase of income per capita. When looking at a standard 2000 hour work year the change represents an average pay raise of 1.13 dollars an hour. per voter per capita Increase per Year 2,250 1,125 Increase per Month 187.5 93.75 Increase per Week 43.27 21.63 Increase per Day 6.16 3.08 Increase per 2000 hour work year 1.13 0.56 This is why you cannot merely look at income levels and how a precinct votes and assume this means people of a particular socio-economic status are voting a certain way. Inquiries & Perspectives 90
This is true even if you have your data on income and voting from the census bureau and overlay them with maps of income. As we all know, correlation does not necessarily mean causation. Gelman, A. (2008). Red state, blue state, rich state, poor state: Why Americans vote the way they do. Princeton: Princeton University Press. Gelman, A. (2012). Voting patterns of America s whites, from the masses to the elites. Downloaded 2016 http://themonkeycage.org/2012/03/voting-patterns-of-americaswhites-from-the-masses-to-the-elites/ Gelman, A., Kenworthy, L, & Su, Y. (2010) inequality and partisan voting in the united states. Social Science Quarterly, 91(s1) 1203-1219 Huber, J., Stanig, P., (2009) Individual income and voting for redistribution across democracies. Downloaded 2016 http://www.columbia.edu/~jdh39/site/research_files/huber_stanig_voting_1.pdf McCarty, N., Poole, K., & Rosenthal, H. (2006) Political polarization and income inequality. Downloaded (2016) http://www.russellsage.org/sites/all/files/u4/mccarty,%20poole,%20%26%20rosenthal_ Political%20Polarization%20%26%20%20Inequality.pdf Inquiries & Perspectives 91